What is "thars" in Dr. Seuss poetry "The Sneetches"?

The Sneetches, by Dr. Seuss:

Now, the Star-Belly Sneetches had bellies with stars.

The Plain-Belly Sneetches had none upon thars.

Those stars weren’t so big. They were really so small.

You might think such a thing wouldn’t matter at all.

What's the meaning of thars in the above context? Is it a dialect form of theirs?

I do not remember much "eye-dialect" style from Dr. Seuss children poetry, at least not in this particular poem. Of course I may have overlooked it. However, at least it is not typical for him. Why would he use it right here? Is it (as Hugh suggest in his comment) to express a sneer? Would Dr. Seuss really use it just of the sake of rhyme, as Sven Yargs suggests in his comment ("to enable the fancy sneetches to have stars on their bellies instead of stairs")?

The word thars is indeed a dialect form of theirs, just as bars (sometimes rendered as "b'ars") is of bears. This pronunciation was extremely widespread in the U.S. West, according to Maximilian Schele de Vere, Americanisms: The English of the New World (1872):

Bar represents in the West almost uniformly the bear, and re-appears in bar-meat.

...

There, or rather thar, as it is more generally pronounced, means, in Western parlance, either the consent given to a proposition, or the familiarity with the subject in question. "Want me to liquor, stranger? I am thar!" (F.B. Harte, Luck of Roaring Camp.)

But any notion that Dr. Seuss is imitating Western U.S. pronunciation of the late nineteenth century in The Sneetches for some larger poetical purpose fails to withstand the most cursory scrutiny. His real interest is in following the track of his rhyme into unexpected and amusing places—and in pursuit of those effects he is by no means above playing fast and loose with normal spellings and pronunciations. Happily, the results of the liberties he takes with normal spelling are often funny and sometimes charming. Thus we have, from How the Grinch Stole Christmas:

Then he slithered and slunk, with a smile most unpleasant,

Around the whole room, and he took every present!

Pop guns! And bicycles! Roller skates! Drums!

Checkerboards! Tricycles! Popcorn! And plums!

And he stuffed them in bags, Then the Grinch very nimbly,

Stuffed all the bags, one by one, up the chimbley!

And from Happy Birthday to You:

"Today," laughs the Bird, "eat whatever you want.

Today no one tells you you cawnt or you shawnt.

And today, you don't have to be tidy or neat.

If you wish, you may eat with both hands and both feet.

So get in there and munch. Have a big munch-er-oo!

Today is your birthday! Today you are you!"

...

As you see, we have here in the heart of our nation

The Official Katroo Birthday Pet Reservation.

From east of the East-est to west of the West-est

We've searched the whole world just to bring you the best-est.

And from On Beyond Zebra:

Then we go on to SNEE. And the SNEE is for Sneedle

A terrible kind of ferocious mos-keedle

Whose hum-dinger stinger is sharp as a needle.

And from elsewhere in The Sneetches (this time, it bears emphasizing, with not the slightest invocation of 19th-century Western U.S. speech patterns):

Then up came McBean with a very sly wink

And he said, "Things are not quite as bad as you think.

So you don't know who's who. That is perfectly true.

But come with me friends. Do you know what I'll do?

I'll make you again the best Sneetches on beaches

And all it will cost you is ten dollars eaches."

So there (said Sven Yargs) you can perfectly see

How the rhymes of Doc Seuss are both lock-step and free.

He writes 'em to march and he writes 'em to halt,

And he writes 'em to tickle your inner gestalt.

And though you may think him as strict as a papa,

He won't scorn a rhyme just because it's not proppa.